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<p>This type of problems is an important building block in series solutions of partial differential equations.(Dirichlet BC) We now attempt to solve the problem in <a href="" class="xref" data-knowl="./knowl/ep1.html" title="Equation 7.2.1">(7.2.1)</a>.</p>
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\begin{equation*}
y^{\prime \prime}+ \lambda y=0,\quad y(0)=0,\quad y(L)=0,
\end{equation*}
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<p class="continuation">The general solution depends on the roots, i.e., on the sign of <span class="process-math">\(\lambda\text{,}\)</span> which has 3 possibilities:</p>
<span class="incontext"><a href="sec7_2.html#p-318" class="internal">in-context</a></span>
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